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In a TV factory 9 persons can assemble 10 tv sets in 20 days

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 09 May 2015, 14:06
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if 9 workers can do 10 tv sets in 20 days (working 7.5 hours each day) then:

10= 9(X) *150; where (X) is the rate of work and 150 is 20 days * 7.5 hours a day. Solving this equation X=1/135

Since the problem states that 2 workers do as much as 3 workers in the first set, we have that: (3*1/135)/2, which is equal to 1/90 (the new rate of work.

Finally, solving for 20 sets and 6 hours worked each day, we will have the following equation:

20= [12*(1/90)] *[D*6], where [12*(1/90)] is the rate of work for 12 people and D is the number of D worked. Solving this equation we have that D=1800/72= 25

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In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 27 May 2015, 09:17
a) 2 men of latter group = 3 men of former group => 12 men of latter group = 18 men of former group

b) 9 men take 150 hours for 10 TVs => 18 men will take 75 hours for 10 TVs

c) 75 hours at the rate of 6 hours/day = 12.5 days for 10 TVs

d) Therefore, (12.5*2) days for 20 TVs = 25 days

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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The question seems slightly heavy because of the number of data points given. Let me simplify it by presenting a stepwise detailed solution

Given
We are given information about two sets of people working. In the first case 9 people assemble 10 TV sets in 20 days working 7.5 hours/day. In the second case we are asked to find the time taken by 12 people to assemble 20 TV sets working 6 hours/day. We are also told that the amount of work done by 2 people in second case is equal to the amount of work done by 3 people in the first case.

Let's see how can we break down this question into simpler bits to get to our answer.

Approach
We know that Work = Rate * Time. For the first set of people we are given the amount of work done and the amount of time taken. We can use this information to find out the rate of work done by 1 person. For the next set of people we are given the amount of work to be done and are asked to find the time taken by them. For finding the time taken we will need the rate of work done by these people.

We are given a relation between the work done by the first set of people and the second set of people. We will use this information and the work rate equation to find out the rate of work done by second set of people and then the time taken by them to complete the work.

Working Out
First set of people

Work done by 9 people = 10 TV sets
Time taken by 9 people each = 7.5 hours for 20 days = \(20* 7.5\) hours

Rate of work done by 9 people = \(\frac{Work}{Time}\) = \(\frac{10}{20*7.5}\)

So, the rate of work done by 1 person \(= \frac{10}{20*7.5*9}\)

Second set of people

Work done by 12 people = 20 TV sets

We are told that 2 people in the latter case do as much work as 3 people in the former. i.e.

work done by 2 persons in the second case = work done by 3 people in the first case.

Since time taken is the same, assuming \(R_{1}\) to be the rate of 1 person in the first case and \(R_{2}\) to be the rate of 1 person in the second case we can write

\(2 * R_{2} * t = 3 * R_{1} * t\) which gives us \(R_{2} = \frac{3}{2} * R_{1} = \frac{3}{2} * \frac{10}{20*7.5*9}\) for 1 person

Rate of work done by 12 people \(= 12 * \frac{3}{2} * \frac{10}{20*7.5*9}\)

Let's assume the number of days it took 12 people to assemble 20 TV sets be \(x\). As the people worked for 6 hours daily,time taken by 12 people each =\(6x\) hours.

Putting the above information in the equation Work = Rate * Time, we get

\(20 = 12 * \frac{3}{2} * \frac{10}{20*7.5*9} * 6x\)

\(x = 25\) days

Hope this helps :)

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Harsh
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 05 Jul 2015, 03:44
VeritasPrepKarishma wrote:
boksana wrote:
In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?

A. 10
B. 12.5
C. 20
D. 25
E. 50


We will solve the question using the method discussed in my post here: http://www.veritasprep.com/blog/2013/02 ... variation/
Look at question 2 in the post.

But before we do that, let's make people in the two cases comparable.
2 people of latter equivalent to 3 people of former.
12 people of latter equivalent to 18 people of former.

So we see that if effect, the number of people has doubled in the latter case.

Days taken = 20 * (9/18) * (20/10) * (7.5/6) = 25 days



Hi karishma,

Can you please explain how you got (20/10) in the above expression?

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 09 Jul 2015, 23:48
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jayanthjanardhan wrote:
VeritasPrepKarishma wrote:
boksana wrote:
In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?

A. 10
B. 12.5
C. 20
D. 25
E. 50


We will solve the question using the method discussed in my post here: http://www.veritasprep.com/blog/2013/02 ... variation/
Look at question 2 in the post.

But before we do that, let's make people in the two cases comparable.
2 people of latter equivalent to 3 people of former.
12 people of latter equivalent to 18 people of former.

So we see that if effect, the number of people has doubled in the latter case.

Days taken = 20 * (9/18) * (20/10) * (7.5/6) = 25 days



Hi karishma,

Can you please explain how you got (20/10) in the above expression?


In the former case, they assemble 10 tv sets and in the latter case they assemble 20 tv sets. Since they assemble more tv's in the second case, days taken will be more so we multiply previous days taken (20) by 20/10.
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In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 15 Aug 2015, 05:27
This problem can be solved in 2 simple steps, if u can understand the relations between the different elements.
Number of men working is directly proportional to work and inversly proportional to time (day and number of hours).
=> m1 * t1 *d1 /w1 = m2 * t2 * d2 / w2 --(1)

Also, 3m1/w1 = 2m2/w2
However w1 = w2,because its the same work.(It takes 3 men in former case and 2 men in latter case to do the same work)
=> 3m1 = 2m2
=>m1/m2 = 2/3
Coming back to eqn (1),
Suppose it takes "D" days to complete the work,
m1 * 9 * 20 * 7.5 / 10 = m2 *12 * D * 6 /20
D= (m1/m2) *37.5
D= (2/3) * 37.5
D= 25 days

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 15 Aug 2015, 05:41
boksana wrote:
In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?

A. 10
B. 12.5
C. 20
D. 25
E. 50


20*(9/12)(20/10)(15/12)(2/3)=25
9/12 because as persons are increased, days will reduce
20/10 because as no of tv sets increased, days will increase
15/12 because as no of working hours reduced, days will increase
2/3 because as efficiency increased, days will reduce.
got it.
Hence, correct option is D

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 20 Aug 2015, 15:01
This is how I think about it. I hope it helps.

We know that doubling the previous workers we can get 20 TVs - if 9 guys gave is 10 TVs, then 18 will give us 20. We also know that 18 former workers = 12 new workers.

18 workers = 20 TVs = 7.5 hour days = 20 Days
12 workers = 20 TVs = 6 hour days = X Days

18 workers = 12 workers in terms of rate only difference is the 18 workers can work 7.5 hour days and 12 works can only work 6 hours.

The 12 workers are working 6/7.5 = 75% less per day and so it will take them 25% longer to finish the task.

20x(5/4) = 25 Days

Hope that's useful!

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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Here's my approach -

Efficiency of 9 former men = 6 latter men
=> 6 latter men make 10 sets in 150 hours
=> 12 latter men make 20 sets in 150 hours = 25 days (Considering 6 hour/day)

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 06 Oct 2015, 04:45
Total man hours spent in assembling 10 TV sets by 9 persons, working 7.5 hours a day=9x20x7.5=1350
Time required to assemble 1 set = 1350/10 =135 hours

To make both the cases comparable
2 persons in the later doing work equivalent to 3 person in former.
12 person in the later doing work equivalent to 18 person in former case.

Daily Effot by 12 men ( doing work equivalent of 18 men) = 18x 6 =108 hours

Time required to assemble 20 TV sets = (135x 20)/108
=25 days
:)
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 09 Oct 2015, 20:48
(20*7.5)*9*R=10
so R=1/135
3R=1/45 equivalent to new 2R, so new R = 1/90
now, (T*6)*12*(1/90)=20
T=25 days

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 15 Oct 2015, 03:37
boksana wrote:
In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?

A. 10
B. 12.5
C. 20
D. 25
E. 50


If 9 can assemble 10 in (20*7.5=) 150 hours, 1 can assemble 10 in (150*9=) 1350 hours.

In the new case, 2 people can work as much as 3 before. So 12 new workers = 18 old workers.

18 old workers could assemble 10 in 75 hrs and 20 in 150 hrs.

Working 6 hours a day, it would take the new workers 150/6 = 25 days.

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 15 Oct 2015, 04:08
boksana wrote:
In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?

A. 10
B. 12.5
C. 20
D. 25
E. 50


being given that 2 persons in the latter case do work as much as 3 men in the former means that in latter case we have 1.5 times efficient men as we did earlier. or in simpler terms we have 12*1.5 = 18 people in second case.

let each tv correspond to 10 units.

now equate man hours

100/(9*20*7.5) = 200/(18*x*6)
=> x = 25.
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 15 Oct 2015, 05:33
I don't understand " in 20 days of 7 1/2 working hours" ??
so I cant solve the question, please help

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 15 Oct 2015, 05:36
zahraf wrote:
I don't understand " in 20 days of 7 1/2 working hours" ??
so I cant solve the question, please help


It means that each of the 9 people works for 7.5 hours per day for 20 days to finish 10 tv sets.

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 09 Nov 2015, 12:49
Is this right ?

- to assemble 20 tv it will take 20/(8/135) = 168.75 hours


I kept getting 337.5 as the answer here.

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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GMATDemiGod wrote:
Is this right ?

- to assemble 20 tv it will take 20/(8/135) = 168.75 hours


I kept getting 337.5 as the answer here.


The questions involving multiple variables in work rate can usually be done in a single step.

But before we solve here, let's make people in the two cases comparable.
2 people of latter equivalent to 3 people of former.
12 people of latter equivalent to 18 people of former.

So in case 1 there were 9 people and in case 2 there were 18 equivalent people

"In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?"

9 people ........10 tv sets.........20 days............7.5 hrs
18 people........20 tv sets.........?? days .............6 hrs

We start with the unknown - the number of days.
The number of days will change. They will become 20 * (9/18) * (20/10) * (7.5/6) = 25 days

20 is the original number of days which needs to be adjusted to factor in the changes in the variables.

You multiply it by 9/18 because when number of people changes from 9 to 18, the number of days will decrease. So you multiply by a number less than 1.
You multiply by 20/10 because when number of tv sets increase from 10 to 20, number of days will increase. So you multiply by a number more than 1.
You multiply by 7.5/6 because when number of hours decrease from 7.5 to 6, number of days required will increase. So you multiply by a number more than 1.

Using this logic, you don't have to worry about how each variable varies with the other. Just use the logic of increase/decrease and less than 1/more than 1.
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 09 Nov 2015, 21:38
oh, wow, good question.
knowing that 9 workers work for 20 days, 7.5h a day - make 10 tv's. we can calculate that they work for 150 hours to make 10 tv's or rate 1/15 for all 9. To find the rate for 1 worker, divide by 9. 1/135. so 1 worker, makes a TV in 135 hours.
Since we know that 2 new workers work as fast as 3 workers, we know that 12 workers would work as fast as 18 old workers.
1/135 multiply by 18 and multiply by 6 (since the new work day will have 6 hours).
18*6/135 - simplify by 3 = 18*2/45, again by 3 - 6*2/15 again by 3 -> 4/5. So the new 12 workers do 4 TV's in 5 days. That means that 20 TV's will do in 25 days.

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In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 28 Mar 2016, 19:14
boksana wrote:
In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?

A. 10
B. 12.5
C. 20
D. 25
E. 50



MDH/W will always be a constant provided the conditions are same.
where
M=no. of men
D=no. of days
H=no. of hours
W = the work done

Here M1= 9, D1= 20, H1 = 15/2 and W1= 10
Given 2/M2=3/M1 => M1 = 3M2/2

Given M2 = 12, so equivalent number of M1 will be 3*12/2=18 ( this is to keep the same efficiency) Hence calculating for 18 M1 is same as calc for 12 M2
so M2=18, D2= n, H2=6 and W2=20

So, since MDH/W is a constant

M1D1H1/W1 = M2D2H2/W2

(9*20*15/2)/10=18*n*6/20
n=25

Hence the option is D. :wink:

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 18 Apr 2016, 11:58
In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?

A. 10
B. 12.5
C. 20
D. 25
E. 50

I was pressed for time(I almost took 3.5 min), So I have to make a quick guess nonetheless I will give both the approaches - quick guess and detailed.
Quick guess:

9 persons took = 20(\(\frac{15}{2}\)) hours
9 guys ---- 10tv sets ---- 150 hrs
12 guys--- 20 tv sets ----- ???? should be "<300" i.e \(\frac{300}{6}\) = must be <50 days

3 guys are extra -- \(\frac{150}{3}\) = 50 hrs , substract from 300 -50 => 250 hrs => \(\frac{250}{6}\) = approx. 25

Semi Detail approach:

we already worked out first two steps .

9 guys ---- 10tv sets ---- 150 hrs => Efficiency per head = \(\frac{1}{15*9}\) = \(\frac{1}{135}\)
12 guys--- 20 tv sets ----- ???? should be "<300" i.e \(\frac{300}{6}\) = must be <50 days

3 guys from 12 are equivalent to 2 guys out of 9, so remove 1 from 12, you should calculate for 11 workers.

=(11*\(\frac{1}{135}\)) * (x) = 20 tv sets (remember that the efficiency is apprxly correct, you are good as long as the options are not very narrow)
=> x = approx 25


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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days   [#permalink] 18 Apr 2016, 11:58

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